"No more dirty dishes shall meet the eye."

Whether it works or not is up to your roommates, but as a native (North American) English speaker, I think it's above average.

If you're a non-native speaker I think you can congratulate yourself on coming up with a pretty reasonable turn of phrase there. But as mickeyf says, it only works if your flatmates get with the program!

It may therefore be slightly nit-picking, but I have to say I think "No more dirty dishes shall meet the eye!" implies "meet your eye" (the flatmate's)...

...and that this implies (since Optimus Prime himself is giving the undertaking) that he will be doing the washing-up. That might be what you'd all like, but frankly I think you'll have a long wait!

Full marks for grammar and content. The archaic tone of the phrasing lends it an air of gravity.

I, too, have my doubts that the slovenly flatmates will shape up (but it pays to think positively).